Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
Αναζήτηση στο βιβλίο
Σελίδα 113
... multiple of the second , that the multiple of the third has to the multiple of the fourth . Let A B C D , and let m and n be any two numbers ; mA : nB :: mC : nD . า Take of mA and mC equimultiples by any number p , and of nB and nD ...
... multiple of the second , that the multiple of the third has to the multiple of the fourth . Let A B C D , and let m and n be any two numbers ; mA : nB :: mC : nD . า Take of mA and mC equimultiples by any number p , and of nB and nD ...
Σελίδα 114
... multiple of a magnitude by any number a multiple of the same magnitude by a less number be taken away , the remainder will be the same multiple of that magnitude that the difference of the numbers is of unity . Let mA and nA be multiples ...
... multiple of a magnitude by any number a multiple of the same magnitude by a less number be taken away , the remainder will be the same multiple of that magnitude that the difference of the numbers is of unity . Let mA and nA be multiples ...
Σελίδα 115
... multiple or a part of the second , the third is the same multiple or the same part of the fourth . Let A B C : D , and first let A be a multiple of B , C is the same multiple of D , that is , if A = mB , C = mD . Take of A and C ...
... multiple or a part of the second , the third is the same multiple or the same part of the fourth . Let A B C : D , and first let A be a multiple of B , C is the same multiple of D , that is , if A = mB , C = mD . Take of A and C ...
Σελίδα 116
... multiple of A + B by m exceeds the multiple of C by n - 1 , but the multiple of A by m does not exceed the multiple of C by n - 1 ; therefore A + B has a greater ratio to C than A has to C ( def . 7. 5. ) . Again , because the multiple ...
... multiple of A + B by m exceeds the multiple of C by n - 1 , but the multiple of A by m does not exceed the multiple of C by n - 1 ; therefore A + B has a greater ratio to C than A has to C ( def . 7. 5. ) . Again , because the multiple ...
Σελίδα 118
... multiples of C and D. Then ( 15. 5. ) A : B :: mA : mB ; now A : BC D , therefore ( 11. 5. ) C : D :: mA : mB . But CD :: nCnD ( 5. 5. ) ; therefore mA : mB :: nC : nD ( 11.5 . ) : where- fore if mA7nC , mB7nD ( 14. 5. ) ; if mA = nC ...
... multiples of C and D. Then ( 15. 5. ) A : B :: mA : mB ; now A : BC D , therefore ( 11. 5. ) C : D :: mA : mB . But CD :: nCnD ( 5. 5. ) ; therefore mA : mB :: nC : nD ( 11.5 . ) : where- fore if mA7nC , mB7nD ( 14. 5. ) ; if mA = nC ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore